Arimaa: Chess for Humans

In the field of artificial intelligence, the most difficult problems for computers to solve are those that involve pattern recognition. Humans are very, very good at recognizing patterns (and will even see them where they don’t really exist). Computers? Not so much. In chess, for example, a human will apply pattern recognition to ignore all possible moves except those most likely to be good; in one study, chess grandmasters who were shown a game in progress could later recreate it completely, but when shown a board that was set up randomly, could no longer do so. Computers, on the other hand, generally win by checking every possible move extremely quickly and calculating the estimated value of each.

Enter Arimaa, the first game designed specifically to be hard for computers to play. While it uses a standard chess set (yes, this is a two player only game), each
piece can move forward, backwards, left, and right (except for the pawn, now called a rabbit, which cannot move backwards). Additionally, pieces can be pushed or pulled, and a turn consists of up to four moves. As a result, the decision tree for Arimaa rapidly grows out of control, which is why the top human players have no difficulty beating the top computer players (and not from lack of effort on the programmer’s part – the prize for creating a program which can defeat the top human players started at $10,000 and has grown from there).

So how does the game work? Take a standard chess set (you can also buy specialized Arimaa sets fairly cheaply) and let each player arrange his pieces any way he wants on the first two rows on his side of the board. On each turn, make up to four moves, where a move is picking up any of your pieces and moving it one space in any orthogonal direction (except, again, that rabbits cannot move backwards) More powerful pieces can push or pull less powerful ones, and a piece that is next to a more powerful enemy piece cannot move unless it is also adjacent to a friendly piece. Relative powers are determined by height: taller pieces are more powerful (so the king, for example, cannot be pushed around by anyone, and the queen can only be pushed or pulled – or immobilized – by the king). There are also four pits placed on the board; any piece standing on a pit that is not adjacent to a friendly piece falls in and is removed from the game. Indeed, there is no capturing in Arimaa; shoving enemy pieces into the pit is the only way to get rid of them.

The game ends when either one player loses all of his rabbits, or one of them makes it to the 8th rank (when it would promote, in chess). Each of the games I’ve played ended when one player made a mistake that allowed the other player to finish advancing one of his rabbits. After playing several times, I still don’t feel as if I really have much of an understanding as to the strategy of the game, aside from “watch out for the big pieces” and “make sure your pieces near the pits have backup”, but it’s an interesting challenge. Now if I could just play well enough to beat the computer..

In addition to the game itself, Amazon has a book on Arimaa strategy; additionally, you can play for free (or just check out the rules) at the Arimaa website.

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{ 3 comments to read ... please submit one more! }

  1. Wow. This kind of turns the ancient game of chess on its ear! Very interesting.

  2. Very interesting game! Thanks for sharing!

  3. Considering that the few times I played chess against a computer, I not sure how good my pattern recognition is. lol Thanks for posting this.

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